Open AccessApproximate Controllability
Author(s) -
Rezzoug Imad,
Oussaief Taki-Eddine
Publication year - 2020
Publication title -
wseas transactions on systems
Language(s) - English
Resource type - Journals
eISSN - 2224-2678
pISSN - 1109-2777
DOI - 10.37394/23202.2020.19.3
Subject(s) - controllability , moment (physics) , mathematics , duality (order theory) , banach space , work (physics) , notice , dual (grammatical number) , zero (linguistics) , set (abstract data type) , moment problem , control (management) , pure mathematics , computer science , physics , statistics , art , linguistics , philosophy , literature , classical mechanics , artificial intelligence , political science , law , principle of maximum entropy , thermodynamics , programming language
The objective of this work is to study the approximate controllability with constraints on the control of the heat equation. To demonstrate the approximate controllability, it suffices to use Hahn Banach theorem and notice that the orthogonal of the set of reachable states at the moment t=0 is reduced to zero. Finally we adapted the method of duality (primal-dual) of Fenchel-Rockafellar to characterize the optimal control